Seurat made paintings in which separate dots of color are pl

Seurat made paintings in which separate dots of color are placed close together on the canvas, and from a distance they merge in the eye to form an image. Consider such a painting with the dots in the painting are separated by 1.7 mm and that the wavelength of the light is ?vacuum = 530 nm. Find the distance at which the dots can just be resolved by each of the following.
(a) the eye (pupils diameter 2.5 mm)
m

(b) a camera (aperture diameter 25 mm)
m

Please provide answer

Solution

Angular resolution:

sin = 1.22(/d)

(a) the eye => d = 2.5x10^-3 m

sin = R/sqrt(R²+L²)

where R is the distance between the dots
and L is the distance from the painting to the eye or camera
Hence,

R/sqrt(R²+L²) = 1.22(/d)

R²/(R²+L²) = (1.22)²/ d²

(R²+L²) = d²R²/(1.22)²
a) the eye (pupils diameter 2.5 mm)

L = sqrt[ d²R²/(1.22)² - R² ]

d = 2.5 mm

R = 1.6mm

= 530 mm

= sqrt [(2.5^2*1.7^2) / (1.22*530)^2 - 1.6^2]

= 0.006573 mm

= 0.006573*10^3 m = 6.57 m

(b) a camera (aperture diameter 25 mm)

L = sqrt[ d²R²/(1.22)² - R² ]

Here only change is d = 25*10^-3 m

L= sqrt [(25^2*1.^2) / (1.22*530)^2 - 1.7^2]

= 0.06573 mm

= 0.06573*10^3 = 65.73 m